The goal of this work is the development of a firm mathematical and experimental foundation that will lead to further understanding of how the lipophilic hormones (thyroxine, triiodothyronine, cortisol, the sex steroids, and vitamin D) distribute between plasma and tissues in vivo. To this end, the proposed research will focus on the following specific objectives: 1) The development of a general mathematical model that will allow prediction of tissue hormone concentrations, for any given hormone and under any given set of conditions, from knowledge of the relevant rate constants and from measurements made in bulk plasma. This undertaking will include a complete mathematical delineation of the conditions under which the free hormone hypothesis is and is not expected to be valid. Computer-assisted technology will be used for this purpose. 2) A determination of the mechanism(s) (i.e., via the free pool or via protein-bound pools) of tissue uptake in vivo for thyroxine, triiodothyronine, cortisol, the sex steroids, and vitamin D. This will require for each hormone measurement of the unbound (free) concentration in plasma (equilibrium dialysis of centrifugal ultrafiltration-dialysis will be used), the rate constants for dissociation from plasma binding proteins (a rapid filtration assay will be used), and the rate constant for tissue uptake of free hormone (an in vitro rat liver perfusion system will be used). These findings will be interpreted in terms of the general mathematical model developed. In addition, whenever there is reason to postulate active transport of free hormone, an attempt will be made to determine the location of that transport (i.e., at the plasma membrane or the nuclear membrane). 3) Documentation of whether changes in factors other than plasma hormone concentrations ever affect intracellular hormone concentrations in vivo. Such factors might include the influx and efflux rate constants or, under certain conditions, the elimination rate constant. As a first step, hepatic uptake of thyroxine in fed vs. fasted rats will be considered. 4) A determination of the generalizability of the concepts of in vivo hormone transport developed here. The nonhormone lipids cholesterol and vitamin E will be considered in these terms. Off rate constants, tissue uptake rate constants, and unbound concentrations in plasma will be measured in anticipation that new insights into the transport and metabolism of these lipids will be obtained.